The use of orthogonal polynomials and orthonormal functions in the calculation of the noncentrality parameter of chi-squared
M. A. Hamdan · Communications in Statistics · 1974
The Helmert transformation of a set of observations is applied to produce a method for calculating the noncentrality parameter of Chi-squared. The Chi-squared criterion is first expressed in terms of simple orthonormal functions. These simple orthonormal functions are then represented as Fourier series in the appropriate set of orthogonal polynomials. Finallv. the noncentrality parameter is expressed in terms of the corresponding Fourier coefficients. The method is illustrated by application to three examples.